If you are looking for just a bikini wax - I don't think it hurts that bad. I get brazilian's done and it is much more painful. If it is your first time or you haven't gone in months, it hurts more. It also depends on how much/how coarse your hair is. I have a friend that won't even wax her eyebrows b/c it is too painful for her. So it also depends on your pain tolerance.
For an area like that, I would suggest paying a little more or going to a "nicer" place. There is more of a chance that the person knows what they are doing. I have gone to a cheaper place, only on a suggestion from a friend and I had no problem. I have also gone to a person's home that had everything set up in a room in her basement. It was professional, just like in a salon. She worked from home around her family needs. It really just depends on the person and their skill/knowledge/experience. I currently go to a nicer place (since I had to find a place on my own without any friend suggestions when I moved here) and I would rather pay a little extra than to risk anything to that area!
Also, don't go there fully grown out. I heard that they will send you home b/c they can't wax full length hair down there and they aren't gong to trim you down. Since you are shaving, you just need to let it grow out a little.
Depending on your hair growth, it should last about a month. A price around $40 to $50 would seem reasonable to me (for a brazilian - just a bikini would be cheaper). I have seen them as low as $25.00.
I live north of SLC, so I can't help you out with a location. I would suggest just calling around. When I first moved to Utah, that is what I did.
GL!